Isometry Structures on Vector Bundles

TL;DR

This paper demonstrates that vector bundles over manifolds with free isometric actions can be endowed with principal bundle structures, revealing new geometric relationships.

Contribution

It establishes that the total space of such vector bundles naturally admits principal bundle structures, expanding understanding of their geometric properties.

Findings

Vector bundles over manifolds with free isometric actions have principal bundle structures.

New principal bundle structures can be constructed from the total space of given vector bundles.

The results deepen the connection between vector bundle theory and principal bundle geometry.

Abstract

In this paper, we prove that total space of every vector bundle with the base manifold on which the canonical isometric action acts freely, also carries a principal bundle structure. We also obtain another principal bundle based on the total space of given vector bundle.